When a sound wave and a polarized light wave move collinearly in certain anisotropic crystals, the plane of polarization of the light wave is rotated, provided that the equation .vertline. K.sub.o .vertline. - .vertline. K.sub.e .vertline. = .vertline. K.sub.a .vertline. is satisfied, where K.sub.o, K.sub.e, and K.sub.a are the momentum vectors for the ordinary, extraordinary and acoustic waves, respectively.
Acousto-optical filters, which make use of this phenomenon, have been made from fused silica, lithium niobate (LiNbO.sub.3), and calcium molybdate (CaMoO.sub.4). The fused silica device is described by J. A. Kusters, D. A. Wilson, and D. L. Hammond in a paper entitled "Selection Rules for Optimum Crystallographic Orientation in Acoustically Tuned Optical Filters," submitted to Journal of the Optical Society, 1973. The lithium niobate filter is described by S. E. Harris and R. W. Wallace in an article entitled "Acousto-Optic Tunable Filter," Journal of the Optical Society of America, Vol. 59, No. 6, pages 744 to 747, (June 1969). Another version of the lithium niobate filter is described in an article entitled "Electronically Tunable Acousto-Optic Filter" by S. E. Harris, S. T. K. Nieh, and D. K. Wilson, Applied Physics Letters, Vol. 15, No. 10, pages 325 to 326, Nov. 15, 1969). The calcium molybdate filter is described in "CaMoO.sub.4 Electronically Tunable Optical Filter," by S. E. Harris, S. T. K. Nieh, and R. S. Feigelson, Applied Physics Letters, Vol, 17, No. 5, pages 223 to 225 Sept. 1, 1970). Also, a tellurium dioxide filter, which is not collinear, is described by I. C. Chang, in "Non-Collinear Acousto-Optic Filters," IEEE Journal of Quantum Electronics, Vol. QE-9, No. 6, pages 660 to 661 (June 1973). Also see "Electronic Tuning of a Dye Laser Using the Acousto-Optic Filter," by D. J. Taylor, S. E. Harris, and A. T. K. Nieh in Applied Physics Letters, Vol. 19, No. 8, pages 269 to 271, Oct. 15, 1971.
The usefulness of a particular material in an acousto-optical filter depends upon several factors. The material should have a transparency range appropriate to the range of wavelengths which are of interest. The transmission range of the materials of which filters have been made extends to only about 4.5.mu.m in the infrared.
The material should also have a low acoustic drive power density requirement for 100% transmission at the peak of the transmission band so that it can be operated with as little power as possible. The acoustic drive power density P.sub.A /A (where P.sub.A is the acoustic power and A is the area) required to achieve 100% optical transmission at the peak light wavelength of the filter response, .lambda..sub.o is given by: ##EQU1## where L is the length of the crystal, .rho. is the density, V is the acoustic velocity, n.sub.o and n.sub.e are the refractive indices of the ordinary and extraordinary rays, respectively, and p.sub.ij is the appropriate photoelastic coefficient. The power density can also be given by ##EQU2## where M.sub.2 is the acousto-optic figure of merit ##EQU3## Thus, a high acousto-optic figure of merit will result in a low drive power density requirement.
A low drive power density requirement for 100% transmission at the peak of the filter passband is very important at the longer infrared wavelength because the drive power density requirement increases as the square of the optical wavelength of the filter. Thus, a filter operating at 3.5.mu.m requires 25 times the drive power density of a filter centered at 0.7.mu.m, other parameters being equal ((3.5/0.7).sup.2 = 25).